Battle Challenge: Who isn't set up to fight? At least a little? Who negotiates their way through all the provinces? That gets VERY expensive. With a Traz and the normal military buildings, you can quickly build up more units that you'll ever need. And units you lose are cheap and easy to buy again.
Production Challenge: If you've been playing for a while, you gradually acquire a collection of event production buildings (Gondola Dock Market, Cider Mill, Aviary, Bazaar, Mad Scientist's Lab, Santa's Workshop, Soccer Field, etc.) or Terrace Farms. If the challenge wants 24-hr productions, make yourself some FPs - like you were probably going to do anyway. If it wants 5-min productions, it should take you less than an hour total. etc.
Sector Challenges: You're going to need the sectors eventually anyway. If you're ahead of your age on the map, that just means you've got some tech research to do - which you're also going to eventually do anyway.
The point is, all the other challenges take some effort (as they should), but cost relatively little, materially. But goods are much more expensive than coins and supplies. And goods buildings take up more space in your city - which let's face it, is the most valuable commodity of all in this game.
And what if they're asking for goods from the previous era, that you don't have thousands of, because you had to use them to make Promethium? Sure, I'd be happy to negotiate away my OF goods all day long. But AF goods are particularly hard to come by lately. Yes, I could rebuild some previous-age goods buildings, but that makes it even more expensive - in the most valuable commodity in the game.
And yes, so far, every Negotiation Challenge I've seen has asked for (at least some) AF goods (my previous age) which I do not have thousands of lying around. And some of the VF techs require more Promethium to unlock. And some of the VF sectors need Promethium to negotiate (in case I have to do that).